I agree with you. I think the term engineer is one of prestige, maybe not to the degree of a doctor to most, but still. I feel there are certainly software engineers out there, but the vast majority who title themselves as such could probably live with something more apt like software developer in what they actually do from day to day if they set aside their pride. As competitive as the hiring market can be in the tech sector, employers do their own marketing with the whole "I'll make you sound more important than you are" or "we're so cool and hip we're going to call you a ninja or unicorn". It does muddy up and cheapen the term engineer, as there are companies that are looking for true engineers and suddenly you have a code monkey who's been titled a software engineer in his last job thinking that he can handle it.
I guess when I think of engineering in classical terms, I think of someone building and maintaining something tangible and often complex. These days we can apply that same mentality to software, but let's be honest unless you are actively planning, or seeing the big picture and trekking into undocumented territory, you're most likely just a software/web/backend/frontend developer, similar to construction workers as far as being task oriented and putting the pieces into their right places. Okay, maybe a little bit more than construction workers in that regard, but certainly no engineer.
, you can. In fact, almost anyone can take the FE...if they feel like paying $225 for the exam. The NCEES doesn't really care. They are simply a testing body. 
